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**Hint:**We know that a number is a prime number when it has two positive divisors i.e. 1 and itself and a number is a composite number when it has more than two positive divisors and at least one of the divisors is not 1 and itself. Now, check the options given in the question which are neither prime nor composite.

__Complete step-by-step answer__:We are asked to find the option which is neither prime nor composite. We know that a prime number is a number which has only two positive divisors i.e. 1 and itself.

A composite number is a number which has at least one its divisors not 1 or the number itself,

Now, we are going to check the options given in the above problem whether they are neither prime nor composite.

Checking option (a) 0 we get,

0 is not a prime number because there are infinite factors which we multiply by 0 gives 0 so the definition of prime number which has only two factors 1 and itself is not satisfying.

0 is not a composite number because it is not a positive integer which is not satisfying the fundamental arithmetic and 0 cannot be divided by itself then we will get $\dfrac{0}{0}$ which is an indeterminate form.

Hence, 0 is neither prime nor composite.

Hence, option (a) is correct.

Checking option (b) 1 we get,

1 is not a prime number because for a prime number the number should have two divisors 1 and itself. Now, 1 has only one divisor i.e. 1.

1 is not a composite number because a number to a composite number when it has a divisor which is not 1 and itself so here 1 has only one divisor i.e. 1.

Hence, 1 is neither a prime nor a composite number.

Hence, option (b) is correct.

Checking option (c) 2 we get,

2 is a prime number because it has two positive divisors 1 and 2 which is satisfying the definition of a prime number.

2 is not a composite number because it has not divisors which are other than 1 or itself.

Hence, 2 is a prime number but not a composite number.

Checking option (d) 5 we get,

5 is a prime number because it has two positive divisors 1 and 5 which is satisfying the definition of a prime number.

5 is not a composite number because it has not divisors which are other than 1 or itself.

Hence, 5 is a prime number but not a composite number.

**From the above options, the correct option is (a) and (b).**

**Note**: You might think 0 is a composite number because it has an infinite number of factors which on multiplication by 0 will give 0 but here 0 cannot be divisible by itself that’s why 0 is not a composite number.

You also might think that 1 is a prime number as if we multiply 1 by itself we get 1. But as you can see that the divisor 1 is creating ambiguity here like whether 1 is the number itself or the number 1 so 1 is not a prime number.

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